In a Mach-Zehnder (MZ) interferometer, an optical signal is split and passed along two optical paths before recombining. Each optical path lies along a different branch of the transmission medium, and may have different optical lengths due to different refractive indices of the medium in each branch. On recombining, different frequencies of the optical signal will interfere to different degrees, depending on the difference in optical length between the two paths. At frequencies for which the different optical lengths result in a phase difference of .pi. radians the signals along each branch will destructively interfere at the output of the MZ interferometer. At frequencies for which the different optical lengths result in no phase difference the signals along each branch will constructively interfere.
In an MZ modulator, a voltage is applied to the two branches of the interferometer. This alters the relative refractive indices of the branches, thereby altering their relative optical lengths. The amount of constructive interference for a particular frequency (typically a carrier frequency of the optical signal) at the output of the MZ modulator can be varied by varying the voltage applied to the two branches. By modulating the applied voltage, the optical signal can be modulated. The relationship between the applied voltage and the output power at a particular frequency can be represented by a Mach-Zehnder transfer function (see FIG. 1).
The halfwave voltage, V.sub..pi. (or Vpi), of an MZ modulator is defined as the difference between the applied voltage at which the signals in each branch of the MZ modulator are in phase and the applied voltage at which the signals are .pi. radians out of phase. In other words, V.sub..pi. is the voltage difference between maximum and minimum output signal power (see FIG. 1). In order for an MZ modulator to be used most efficiently in a communications network it is necessary to know the value of V.sub..pi. accurately. The V.sub..pi. of an MZ modulator is an important parameter, for example, for determining RF-driver settings.
If the applied voltage is an AC voltage, as it must be to modulate the optical signal, then the halfwave voltage becomes difficult to determine. The voltage is applied along travelling wave electrodes which are parallel to the optical transmission medium. Ideally the voltage wave travels along each electrode such that the optical signal is adjacent to a constant voltage while within the MZ modulator. However in reality the voltage seen by the optical signal is not constant, due to attenuation of the voltage along the electrodes and to the difference between the group velocities of the electrical and optical signals. The V.sub..pi. used by the RF-driver to effect 180.degree. phase shifts cannot be determined from the ideal V.sub..pi. for applied DC voltages, but rather must be dependent on the modulation frequency. This halfwave voltage is called the AC halfwave voltage, V.sub..pi. -AC (or Vpi-AC).
One method of determining V.sub..pi. -AC at all modulation frequencies would be to determine V.sub..pi. -AC accurately at one modulation frequency, and then use the measured small signal frequency response of the MZ modulator to calculate the V.sub..pi. at other frequencies. The measured small signal frequency response of the MZ modulator is generally lower than the theoretical frequency response, due to the losses which occur with AC modulation. Commercial network analyzers can be used to measure the small signal frequency response of an MZ modulator over modulation frequency ranges of about 130 MHz to 30 GHz.
One existing technique for measuring V.sub..pi. -AC uses modulations having a high peak-to-peak voltage, but these are difficult to implement at high frequencies and require the use of specialized equipment. Another technique uses variations in amplitude of a square wave modulation. However this technique relies on eyeballing. The technique is limited by the accuracy of the eyeballing, and square wave modulation is not a scientifically accurate method of determining signal parameters due to the multitude of harmonics making up the waveform.
There is therefore a need for a method of measuring V.sub..pi. -AC more accurately, more consistently, and in a simpler manner.